In order to determine the composition and structure of an underground formation, seismic data may be utilized. As understood in the art, when a seismic wave propagates through the earth from a source to a receiver, the received seismic wave may bring information about geophysical properties of the subsurface volume. The properties may include, without limitation, seismic wave velocity, mass density, and anisotropy properties. In exploration geophysics, by recording the seismic waves at the surface by one or more geophones or hydrophones, a model of the subsurface strata may be determined through various seismic processing techniques.
The time between transmission of the seismic wave and reception of the reflected seismic waves may be measured to determine the distance to an interface. More advanced techniques, such as reflection velocity tomography, are capable of using kinematic information contained in the seismic reflection data to transform the seismic data gathered from the reflected waves to determine a more detailed and complete model of the underground seismic velocity model. Another technique, known as full waveform inversion (FWI), utilizes full waveform information, i.e. both phase and amplitude data, both transmission seismic data and reflection seismic data, both primaries and multiples, contained in the seismic data gathered from the recorded seismic waves to generate a high resolution velocity model or other geophysical property model of the underground formation through optimal data fitting.
Because of hardware limitations of geophones and hydrophones, seismic data is typically band limited, rendering low frequency seismic data unavailable. Due to the lack of low frequency data, large underground structures are less able to be identified due to issues including without limitation nonlinearity of the FWI and the cycle-skipping phenomenon. Nonlinearity and cycle-skipping can result in incorrect data fitting as, for example, the inversion may be trapped in local minima, preventing the updated models from progressing properly. Nonlinearity and cycle-skipping each increase in effect and likelihood with increasing frequency during an inversion operation.